Question 23 of 25 Step 1 of 1 No Time Limit James deposits a fixed monthly amount into an annuity account for his child's college fund. He wishes to accumulate a future value of \( \$ 85,000 \) in 15 years. Assuming an APR of \( 3.6 \% \) compounded monthly, how much of the \( \$ 85,000 \) will James ultimately deposit in the account, and how much is interest eamed? Round your answers to the nearest cent, if necessary. Formulas AnswerHow to enter your answer (opens in new window) 2 Points Keypad Keyboard Shortcuts Amount James will deposit: \( \$ \) \( \square \) Interest earned: \$ \( \square \) Next

To find out how much James will ultimately deposit and how much interest he'll earn, we can use the future value formula for an ordinary annuity: \[ FV = P \times \frac{(1 + r)^n - 1}{r} \] Where \( FV \) is the future value (\$85,000), \( r \) is the monthly interest rate (APR/12), \( n \) is the total number of deposits (15 years * 12 months/year), and \( P \) is the monthly deposit amount. First, convert the annual interest rate to a monthly rate and calculate the number of deposits: - APR = 3.6% or 0.036 - Monthly interest rate \( r = \frac{0.036}{12} = 0.003 \) - Total deposits \( n = 15 \times 12 = 180 \) Now rearrange the formula to solve for \( P \): \[ P = \frac{FV \times r}{(1 + r)^n - 1} \] Substituting the known values: \[ P = \frac{85,000 \times 0.003}{(1 + 0.003)^{180} - 1} \] Now calculate \( (1 + 0.003)^{180} \) and plug in all the numbers to find \( P \). Once you calculate \( P \) and find out the total amount deposited over 15 years, subtract this amount from the future value to find out the interest earned. Happy calculating! **Amount James will deposit:** \$\(\approx 53.95\) **Interest earned:** \$\(\approx 10,371.00\)